No, these are generally not the same, though may be considered at the same time. The project risks are those risks which affect the project outcomes (on time, on budget, with acceptable performance).
Product risks include those risks associated with the use of the product. For example, your toaster made in North America will probably have a "UL" symbol on the electrical cord indicating it meets Underwriter Laboratories approval.
Risks of the product are often first thought about by product management when determining the products to move forward with and need to be fully considered during the design of the product. The PM needs to consider how these requirements (e.g. UL approval) will affect the project timeline and budget.